Problem 41 - College Algebra

Question

Add or subtract terms whenever possible. $$3 \sqrt{18}+5 \sqrt{50}$$

Step-by-Step Solution

Answer

The combination of the given terms is simplified to \(34\sqrt{2}\).

Step 1: Prime Factorization and Root Extraction

First, break down each term into prime numbers under the square root: \[3 \sqrt{18} = 3 \sqrt{9*2} = 3 * \sqrt{9} * \sqrt{2} = 3 * 3 * \sqrt{2} = 9\sqrt{2}\] Similarly, \[5 \sqrt{50} = 5 * \sqrt{25*2} = 5 * \sqrt{25} * \sqrt{2} = 5 * 5 * \sqrt{2} = 25\sqrt{2}\]

Step 2: Combine Like Terms

The resulting expressions from step 1 now have common root terms (\(\sqrt{2}\)), and can be added together: \(9\sqrt{2} + 25\sqrt{2} = 34\sqrt{2}\).

Step 3: Final Simplification

Since it's not possible to simplify the square root of 2 any further, then the final simplified version of the given expression is \(34\sqrt{2}\).